Abstract.
We consider a proper submarkovian resolvent of kernels on a Lusin measurable space and a given excessive measure ξ. With every quasi bounded excessive function we associate an excessive kernel and the corresponding Revuz measure. Every finite measure charging no ξ–polar set is such a Revuz measure, provided the hypothesis (B) of Hunt holds. Under a weak duality hypothesis, we prove the Revuz formula and characterize the quasi boundedness and the regularity in terms of Revuz measures. We improve results of Azéma [2] and Getoor and Sharpe [20] for the natural additive functionals of a Borel right process.
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Received: 30 April 1997 / Revised version: 17 September 1999 /¶Published online: 11 April 2000
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Beznea, L., Boboc, N. Excessive kernels and Revuz measures. Probab Theory Relat Fields 117, 267–288 (2000). https://doi.org/10.1007/s004400050007
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DOI: https://doi.org/10.1007/s004400050007